Conclusions: the methodology proposed here shows that for the hilly city of Coimbra, Portugal, centrality, more than relief, is the chief factor determining a location’s pedestrian accessibility. This methodology, based on classic definitions of accessibility as disutility and using on human effort (as measured by muscular energy spent to walk the streets network) as impedance, is general and can be applied to any city. Since human effort rises considerably with slope, it especially adequate to hilly cities.This article presents an approach to pedestrian accessibility based on human effort rather than distance. By measuring effort as the muscular energy required to traverse network arcs with slopes, it is possible to derive an accessibility indicator that takes relief into account. A case study in the city of Coimbra, Portugal, shows that while relief does have a considerable impact on the accessibility thus measured, that impact is global and not local. When accessibility to all types of opportunities are considered, the influence of relief ultimately dilutes due to the geographical scattering of those opportunities.info:eu-repo/semantics/publishedVersio

Moreira, Florbela

Rodrigues, João Coutinho

Sousa, Nuno

The Repositório Aberto

Energy for Sustainability International Conference 2017 
Designing Cities & Communities for the Future 
Funchal, 8-10 February, 2017 
 
 
AN ENERGY-BASED PEDESTRIAN ACCESSIBILITY INDICATOR 
N. Sousa12*, F.A. Moreira23 and J. Coutinho-Rodrigues24 
1: Departamento de Ciências e Tecnologia 
Universidade Aberta, Delegação de Coimbra 
R. Alexandre Herculano, 52 
3000-019 Coimbra, Portugal 
e-mail: nsousa@uab.pt,  web: http://www.uab.pt  
2: Instituto de Engenharia de Sistemas e Computadores de Coimbra 
Edifício do Departamento de Eng.ª Electrotécnica e de Computadores 
Universidade de Coimbra 
Rua Sílvio Lima, Polo II 
3030-290 Coimbra, Portugal 
web: http://www.uc.pt/en/org/inescc 
3: Energy for Sustainability, MSc Student 
Faculdade de Ciências e Tecnologia 
Universidade de Coimbra 
Rua Luís Reis Santos, Pólo II 
3030-788 Coimbra, Portugal 
e-mail: moreira.florbela@gmail.com 
4: Departamento de Eng.ª Civil 
Faculdade de Ciências e Tecnologia 
Universidade de Coimbra 
Rua Luís Reis Santos, Pólo II 
3030-788 Coimbra, Portugal 
e-mail: coutinho@dec.uc.pt,  web: http://www.uc.pt/fctuc/dec 
 
Keywords: Walking, Pedestrian, Accessibility, Energy, Sustainability, Coimbra 
Abstract This article presents an approach to pedestrian accessibility based on human 
effort rather than distance. By measuring effort as the muscular energy required to 
traverse network arcs with slopes, it is possible to derive an accessibility indicator that 
takes relief into account. A case study in the city of Coimbra, Portugal, shows that while 
relief does have a considerable impact on the accessibility thus measured, that impact is 
global and not local. When accessibility to all types of opportunities are considered, the 
influence of relief ultimately dilutes due to the geographical scattering of those 
opportunities. 
 
 
 
Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J. 
 
2 
 
1. INTRODUCTION 
Walking is the most basic transport mode, used by practically everybody, every day. It 
connects key city locations among them and provides the basic link to all other modes of 
transport. There has been, in the last decades, an increasing interest in active travel modes, 
like walking or cycling, prompted by sustainability worries, traffic congestion and health 
issues [1]. Indeed, in recent studies dedicated to the evaluation of the performance of 
European cities, the percentage of journeys to work not done by car was considered a quality 
of life indicator [2]. The walk mode is favored for small trips, of up to 1 km [3] [4], a distance 
which is expected to increase if proper infrastructural facilities are provided [5]. It increases 
physical activity, is non-polluting and socially inclusive, and poses little danger to others. 
Because walking is also the most basic travel mode, it will always have a considerable share 
among all transport modes, for people of all ages and social status. It is therefore natural and 
desirable that municipal decision makers have tools to evaluate how their city stands when it 
comes to walking accessibility. 
 
The literature is rich in pedestrian accessibility studies, but very few take relief into account. 
It to fill this gap in the literature, and in a context of rising importance of the walk mode, that 
the present study is presented, as a prototype of a methodology to help municipal authorities 
evaluating pedestrian accessibility of their hilly cities. This research was carried out in the 
context of a case study in the hilly city of Coimbra, Portugal, and used Geographical 
Information Systems as main calculation tool. 
2. METHODOLOGY AND CASE STUDY 
There are many ways to define the concept of accessibility in the literature. This study 
takes the approach of [6], which considers accessibility as a disutility (lower = better). The 
definition used throughout this study is 
 𝐴 𝑖 = 𝑤%𝐼'%()%*(       (1) 
 
where A(i) is the accessibility of geographic location i (trip origin), N is the number of 
types of opportunities (trip destinations), wj is a weight assigned to opportunities of type j, 
and Iij(1) the impedance from location i to the closest opportunity of type j. The formula 
reads as follows: when people at location i walk to interaction opportunities of a certain 
type, j (bakery, restaurant, school, etc.), they will look for the closest one (hence the 
superscript ‘1’), as walking is time-consuming and can be fatiguing in hilly cities. 
Weights are assigned to reflect how often a certain opportunity type is sought-after, with 
higher weights meaning higher frequency and hence higher importance. 
 
To obtain A(i) values it is thus necessary to define locations, indicate where opportunities 
are, and, more importantly, define the impedance function. In a flat city it is natural to use 
Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J. 
 
3 
 
distance as impedance. In a hilly city, however, the slopes people have to walk through 
cause significant increases in energy use by the pedestrian. This is valid both uphill and 
downhill, as high downhill slopes require breaking, a muscular activity which in turn 
requires energy, albeit less than climbing. For this reason, impedance was taken instead to 
be human effort, measured in muscular energy to cross the arcs of the streets network. 
Taking human effort as impedance instead of distance constitutes the main novelty of this 
study. 
2.1. GIS programming 
The GIS setup and calculations were carried out in the ESRI ArcGIS environment, using data 
available from previous projects (streets network, public facilities). To define the locations i, a 
fishnet of 50 m ´ 50 m squares was defined, together with its centroids. Squares whose 
centroid laid more than 100 m away from a network arc were deleted. This step, which is 
optional, leads to removal of squares in faraway or deserted locations and prevents distortions 
due to excessive snapping from centroids to network arcs in the routing calculations of next 
section. Urban public facilities locations were arranged into sets of type j opportunities and 
the streets network was endowed with information concerning human effort to cross each of 
its arcs, in the From-To (FT) and To-From (TF) directions (impedance). To model the 
impedance, the experimental polynomial regression formula of [7] was used: 
 + ,-..0 = 280,5	𝑠8 − 58,7	𝑠; − 78,3	𝑠= + 51,9	𝑠A + 19,6	𝑠 + 2,5  (2) 
 
where 𝐸(𝑠)/kg.m is the energy (in J) per SI unit weight and length required to cross an 
arc of slope (incline) s. Note that the slope can be positive or negative, and the formula 
caters for that. Small downhill slopes lower the walking effort required, down to a 
minimum around –15% slope, and higher downhill slopes force the person to spend extra 
muscular energy for breaking.  
 
To program of this formula in ArcGIS, use was made of altimetric information already 
available in the streets network shapefile for each individual arc, namely average uphill 
and downhill slopes (𝑠JK, 𝑠LMNO) (both marked as positive quantities in the network 
associated table) and respective 3D length (𝑙JK, 𝑙LMNO), in the FT direction. Using tool field 
calculator, human effort necessary to cross each arc, as defined by (2), was calculated for 
FT and TF directions via the formulas: 
 𝐸QR = 𝐸 𝑠JK 𝑙JK + 𝐸 −𝑠LMNO 𝑙LMNO ×80	kg𝐸RQ = 𝐸 −𝑠JK 𝑙JK + 𝐸 𝑠LMNO 𝑙LMNO ×80	kg   (3) 
 
The 80 kg factor (average weight of pedestrian) was inserted so that the formula returns 
energy units. This multiplication is not strictly necessary, as 80 kg is just an overall 
multiplicative factor affecting all arcs. The minus signs reflect the fact that what is uphill 
Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J. 
 
4 
 
in the FT direction becomes downhill in the TF direction, and vice-versa. 
 
Finally, arcs with uphill or downhill slopes higher than 50% were restricted. This allows 
pedestrians to use stairways, whose slopes are circa 45%, but no higher inclines, which 
may be too cumbersome to step through. This completed GIS programming. 
2.2. Pedestrian accessibility indicator map 
With the network programmed, it was possible to calculate the A(i) accessibility indicator. 
For this purpose, the following methodology was used. The public facilities feature class 
was divided into the opportunities types shown in table 1 below, together with their 
respective weight. 
Table 1. Opportunities types and weights. 
Opportunity type Weight Opportunity type Weight 
Cultural associations 1 Shopping centers 2 
Sports halls 1 Entertainment places 2 
City Hall 1 Secondary school 2 
Post offices 1 Pharmacies 2 
Higher education faculties 1 Restaurants 2 
Police squads 1 Grocery stores 3 
Churches 1 Bakeries 3 
Civil parish 1 1st cycle primary schools and kindergarten 3 
Elderly care centers 1 2nd and 3rd cycle primary schools 3 
Primary health care 2   
 
To obtain the individual Iij(1) impedances, the ArcGIS network analyst tool closest facility 
was used to generate shortest routes from each centroid of square i to the set of 
opportunities of type j, with walking energy as impedance. The procedure was repeated 
for the N = 19 opportunities types, leading to 19 walking energy values stored in new 
fields of the feature class of 50 m ´ 50 m squares. Then, using field calculator, formula 
(1) was implemented in a new field of this feature class, leading to the final value A(i) for 
each square. The result, visualized as a map in GIS, is shown in figure 1 below, together 
with the topography of Coimbra, for comparison. The same color scale was used to 
indicate min/max values for both altitude and accessibility. Since the accessibility index is 
expressed in weighted units, its absolute value is arbitrary and this is why the scale 
presented is merely qualitative. 
2.3. Discussion 
The maps evidence considerable discrepancies between altitude and pedestrian accessibility, 
which was to be expected because the pedestrian accessibility index A(i) is affected by both 
distance to opportunities and city relief, not just the latter. The main observation 
concerning accessibility is that the city center evidences the best index values, reflecting 
the effect of centrality, with many nearby opportunities of each type. The hill-top of 
Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J. 
 
5 
 
Olivais (center-top right) in particular displays very good pedestrian accessibility despite 
its high altitude. This is however a very densely populated and well serviced area. 
 
    
Figure 1. Topography of Coimbra (left) and effort-based walking accessibility map (right). 
The geographical dispersion of the opportunities throughout the city also contributes to 
the good performance of the indicator: indeed, while some opportunities require climbing, 
others require descending. In the end, the index for central locations is not excessively 
penalized by relief effects. On the other end of the spectrum lie the faraway regions of the 
outskirts. These have worse indexes, but this is essentially related to lack of close 
opportunities rather than relief effects.  
 
The relief effect is however not negligible: it is present as a background value throughout 
the study area and becomes more explicit for some higher locations within the central 
area. For instance, the University campus ‘Polo I’ zone (center of map, near the river) 
exhibits slightly lower accessibility, owing to being on the top of a hill. The same happens 
in a few other central locations, which would show better indexes if their altitude were 
lower. 
3. CONCLUSIONS AND FUTURE WORK 
The methodology proposed here shows that for the hilly city of Coimbra, Portugal, 
centrality, more than relief, is the chief factor determining a location’s pedestrian 
Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J. 
 
6 
 
accessibility. This methodology, based on classic definitions of accessibility as disutility 
and using on human effort (as measured by muscular energy spent to walk the streets 
network) as impedance, is general and can be applied to any city. Since human effort rises 
considerably with slope, it especially adequate to hilly cities.  
 
For hilly cities, effort/energy-based pedestrian accessibility maps are, in principle, more 
accurate than maps based purely on distance. Therefore, these maps should be preferred 
by municipal authorities when planning for changes to public transportation routes. For 
the case of Coimbra, busses from the outskirts into the (high accessibility) riverside 
downtown are frequent, but this is not the case for the Olivais area, whose high pedestrian 
accessibility indexes indicate it should perhaps be better serviced. Such maps also indicate 
the best zones to improve sidewalks and crossings, thus providing people with adequate 
infrastructure for exerting their choice for the pedestrian mode, which is key to foster that 
choice. 
 
As future work, it would be interesting to apply the methodology to other hilly cities and 
compare altitude charts with the resulting pedestrian accessibility map, so as to check to 
what extent the conclusion that centrality dominates over relief effects holds. Another 
possible line of research would be to set all slopes to zero, recalculate the pedestrian 
accessibility index and create a ‘flat vs real’ differential map. This map would identify the 
geographic locations i for which relief is more relevant. The impedance function can also 
be refined by including sidewalk availability and pavement condition, both of which can 
influence effort. The effort/energy-based approach also allows for construction of other 
types of pedestrian accessibility indexes, such as e.g. number of opportunities within 
standard walking distances (say 600 m), converted into energy equivalent. Finally, since 
long trips can induce tiredness, to validate the accuracy of the hypothesis that human 
effort is cumulative, real experiments can be carried out, that involve volunteer 
pedestrians carrying out a smartphone and a wearable health device to log energy 
expenditure. (Doing this for short trips would only reproduce the results of [7].) 
ACKNOWLEDGEMENTS 
This work was partially supported by the Portuguese Foundation for Science and 
Technology under grant PEst-OE/EEI/UI308/2014. 
REFERENCES 
[1] J. Woodcock, D. Banister, P. Edwards, A.M. Prentice and I. Roberts, “Energy and 
transport”, Lancet Vol. 370, No. 9592, pp. 1078-1088, (2007). DOI: 10.1016/S0140-
6736(07)61254-9 
[2] P. Morais and A.S. Camanho, “Evaluation of performance of European cities with the 
aim to promote quality of life improvements”, Omega Vol. 39, No. 4, pp. 398-409, 
(2011). DOI: 10.1016/j.omega.2010.09.003 
[3] H. Millward, J. Spinney and D. Scott, “Active-transport walking behavior: 
Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J. 
 
7 
 
destinations, durations, distances”, J. Transp. Geogr. Vol. 28, pp. 101-110, (2013). 
DOI: 10.1016/j.jtrangeo.2012.11.012 
[4] P.N. Seneviratne, “Acceptable Walking Distances in Central Areas”, J. Transp. Eng. 
Vol. 111, No. 4, pp. 365-376, (1985). DOI: 10.1061/(ASCE)0733-
947X(1985)111:4(365) 
[5] T.M. Rahul and A. Verma. “A study of acceptable trip distances using walking and 
cycling in Bangalore”, J. Transp. Geogr. Vol. 38, pp. 106-113, (2014). DOI: 
10.1016/j.jtrangeo.2014.05.011 
[6] K.T. Geurs and J. Ritsema van Eck, Accessibility measures: review and Applications, 
Rijksinstituut voor Volksgezondheid en Milieu (National Institute of Public Health and 
Environment), RIVM report 408505 006, (2001). Weblink: 
https://rivm.openrepository.com/rivm/bitstream/10029/9487/1/408505006.pdf 
[7] A.E. Minetti, C. Moia, G.S. Roi, D. Susta and G. Ferretti, “Energy cost of walking and 
running at extreme uphill and downhill slopes”, J. Appl. Physiol. Vol. 29, No. 3, pp. 
1039-1046, (1985). DOI: 10.1152/japplphysiol.01177.2001 
 


English

An energy-based pedestrian accessibility indicator

Conclusions: the methodology proposed here shows that for the hilly city of Coimbra, Portugal, centrality, more than relief, is the chief factor determining a location’s pedestrian accessibility. This methodology, based on classic definitions of accessibility as disutility and using on human effort (as measured by muscular energy spent to walk the streets network) as impedance, is general and can be applied to any city. Since human effort rises considerably with slope, it especially adequate to hilly cities.This article presents an approach to pedestrian accessibility based on human effort rather than distance. By measuring effort as the muscular energy required to traverse network arcs with slopes, it is possible to derive an accessibility indicator that takes relief into account. A case study in the city of Coimbra, Portugal, shows that while relief does have a considerable impact on the accessibility thus measured, that impact is global and not local. When accessibility to all types of opportunities are considered, the influence of relief ultimately dilutes due to the geographical scattering of those opportunities.This work was partially supported by the Portuguese Foundation for Science and Technology under grant PEst-OE/EEI/UI308/2014.info:eu-repo/semantics/publishedVersio

Repositório Aberto da Universidade Aberta

Energy for Sustainability International Conference 2017 Designing Cities & Communities for the Future Funchal, 8-10 February, 2017   AN ENERGY-BASED PEDESTRIAN ACCESSIBILITY INDICATOR N. Sousa12*, F.A. Moreira23 and J. Coutinho-Rodrigues24 1: Departamento de Ciências e Tecnologia Universidade Aberta, Delegação de Coimbra R. Alexandre Herculano, 52 3000-019 Coimbra, Portugal e-mail: nsousa@uab.pt,  web: http://www.uab.pt  2: Instituto de Engenharia de Sistemas e Computadores de Coimbra Edifício do Departamento de Eng.ª Electrotécnica e de Computadores Universidade de Coimbra Rua Sílvio Lima, Polo II 3030-290 Coimbra, Portugal web: http://www.uc.pt/en/org/inescc 3: Energy for Sustainability, MSc Student Faculdade de Ciências e Tecnologia Universidade de Coimbra Rua Luís Reis Santos, Pólo II 3030-788 Coimbra, Portugal e-mail: moreira.florbela@gmail.com 4: Departamento de Eng.ª Civil Faculdade de Ciências e Tecnologia Universidade de Coimbra Rua Luís Reis Santos, Pólo II 3030-788 Coimbra, Portugal e-mail: coutinho@dec.uc.pt,  web: http://www.uc.pt/fctuc/dec  Keywords: Walking, Pedestrian, Accessibility, Energy, Sustainability, Coimbra Abstract This article presents an approach to pedestrian accessibility based on human effort rather than distance. By measuring effort as the muscular energy required to traverse network arcs with slopes, it is possible to derive an accessibility indicator that takes relief into account. A case study in the city of Coimbra, Portugal, shows that while relief does have a considerable impact on the accessibility thus measured, that impact is global and not local. When accessibility to all types of opportunities are considered, the influence of relief ultimately dilutes due to the geographical scattering of those opportunities.    Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J.  2  1. INTRODUCTION Walking is the most basic transport mode, used by practically everybody, every day. It connects key city locations among them and provides the basic link to all other modes of transport. There has been, in the last decades, an increasing interest in active travel modes, like walking or cycling, prompted by sustainability worries, traffic congestion and health issues [1]. Indeed, in recent studies dedicated to the evaluation of the performance of European cities, the percentage of journeys to work not done by car was considered a quality of life indicator [2]. The walk mode is favored for small trips, of up to 1 km [3] [4], a distance which is expected to increase if proper infrastructural facilities are provided [5]. It increases physical activity, is non-polluting and socially inclusive, and poses little danger to others. Because walking is also the most basic travel mode, it will always have a considerable share among all transport modes, for people of all ages and social status. It is therefore natural and desirable that municipal decision makers have tools to evaluate how their city stands when it comes to walking accessibility.  The literature is rich in pedestrian accessibility studies, but very few take relief into account. It to fill this gap in the literature, and in a context of rising importance of the walk mode, that the present study is presented, as a prototype of a methodology to help municipal authorities evaluating pedestrian accessibility of their hilly cities. This research was carried out in the context of a case study in the hilly city of Coimbra, Portugal, and used Geographical Information Systems as main calculation tool. 2. METHODOLOGY AND CASE STUDY There are many ways to define the concept of accessibility in the literature. This study takes the approach of [6], which considers accessibility as a disutility (lower = better). The definition used throughout this study is  𝐴 𝑖 = 𝑤%𝐼'%()%*(       (1)  where A(i) is the accessibility of geographic location i (trip origin), N is the number of types of opportunities (trip destinations), wj is a weight assigned to opportunities of type j, and Iij(1) the impedance from location i to the closest opportunity of type j. The formula reads as follows: when people at location i walk to interaction opportunities of a certain type, j (bakery, restaurant, school, etc.), they will look for the closest one (hence the superscript ‘1’), as walking is time-consuming and can be fatiguing in hilly cities. Weights are assigned to reflect how often a certain opportunity type is sought-after, with higher weights meaning higher frequency and hence higher importance.  To obtain A(i) values it is thus necessary to define locations, indicate where opportunities are, and, more importantly, define the impedance function. In a flat city it is natural to use Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J.  3  distance as impedance. In a hilly city, however, the slopes people have to walk through cause significant increases in energy use by the pedestrian. This is valid both uphill and downhill, as high downhill slopes require breaking, a muscular activity which in turn requires energy, albeit less than climbing. For this reason, impedance was taken instead to be human effort, measured in muscular energy to cross the arcs of the streets network. Taking human effort as impedance instead of distance constitutes the main novelty of this study. 2.1. GIS programming The GIS setup and calculations were carried out in the ESRI ArcGIS environment, using data available from previous projects (streets network, public facilities). To define the locations i, a fishnet of 50 m ´ 50 m squares was defined, together with its centroids. Squares whose centroid laid more than 100 m away from a network arc were deleted. This step, which is optional, leads to removal of squares in faraway or deserted locations and prevents distortions due to excessive snapping from centroids to network arcs in the routing calculations of next section. Urban public facilities locations were arranged into sets of type j opportunities and the streets network was endowed with information concerning human effort to cross each of its arcs, in the From-To (FT) and To-From (TF) directions (impedance). To model the impedance, the experimental polynomial regression formula of [7] was used:  + ,-..0 = 280,5	𝑠8 − 58,7	𝑠; − 78,3	𝑠= + 51,9	𝑠A + 19,6	𝑠 + 2,5  (2)  where 𝐸(𝑠)/kg.m is the energy (in J) per SI unit weight and length required to cross an arc of slope (incline) s. Note that the slope can be positive or negative, and the formula caters for that. Small downhill slopes lower the walking effort required, down to a minimum around –15% slope, and higher downhill slopes force the person to spend extra muscular energy for breaking.   To program of this formula in ArcGIS, use was made of altimetric information already available in the streets network shapefile for each individual arc, namely average uphill and downhill slopes (𝑠JK, 𝑠LMNO) (both marked as positive quantities in the network associated table) and respective 3D length (𝑙JK, 𝑙LMNO), in the FT direction. Using tool field calculator, human effort necessary to cross each arc, as defined by (2), was calculated for FT and TF directions via the formulas:  𝐸QR = 𝐸 𝑠JK 𝑙JK + 𝐸 −𝑠LMNO 𝑙LMNO ×80	kg𝐸RQ = 𝐸 −𝑠JK 𝑙JK + 𝐸 𝑠LMNO 𝑙LMNO ×80	kg   (3)  The 80 kg factor (average weight of pedestrian) was inserted so that the formula returns energy units. This multiplication is not strictly necessary, as 80 kg is just an overall multiplicative factor affecting all arcs. The minus signs reflect the fact that what is uphill Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J.  4  in the FT direction becomes downhill in the TF direction, and vice-versa.  Finally, arcs with uphill or downhill slopes higher than 50% were restricted. This allows pedestrians to use stairways, whose slopes are circa 45%, but no higher inclines, which may be too cumbersome to step through. This completed GIS programming. 2.2. Pedestrian accessibility indicator map With the network programmed, it was possible to calculate the A(i) accessibility indicator. For this purpose, the following methodology was used. The public facilities feature class was divided into the opportunities types shown in table 1 below, together with their respective weight. Table 1. Opportunities types and weights. Opportunity type Weight Opportunity type Weight Cultural associations 1 Shopping centers 2 Sports halls 1 Entertainment places 2 City Hall 1 Secondary school 2 Post offices 1 Pharmacies 2 Higher education faculties 1 Restaurants 2 Police squads 1 Grocery stores 3 Churches 1 Bakeries 3 Civil parish 1 1st cycle primary schools and kindergarten 3 Elderly care centers 1 2nd and 3rd cycle primary schools 3 Primary health care 2    To obtain the individual Iij(1) impedances, the ArcGIS network analyst tool closest facility was used to generate shortest routes from each centroid of square i to the set of opportunities of type j, with walking energy as impedance. The procedure was repeated for the N = 19 opportunities types, leading to 19 walking energy values stored in new fields of the feature class of 50 m ´ 50 m squares. Then, using field calculator, formula (1) was implemented in a new field of this feature class, leading to the final value A(i) for each square. The result, visualized as a map in GIS, is shown in figure 1 below, together with the topography of Coimbra, for comparison. The same color scale was used to indicate min/max values for both altitude and accessibility. Since the accessibility index is expressed in weighted units, its absolute value is arbitrary and this is why the scale presented is merely qualitative. 2.3. Discussion The maps evidence considerable discrepancies between altitude and pedestrian accessibility, which was to be expected because the pedestrian accessibility index A(i) is affected by both distance to opportunities and city relief, not just the latter. The main observation concerning accessibility is that the city center evidences the best index values, reflecting the effect of centrality, with many nearby opportunities of each type. The hill-top of Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J.  5  Olivais (center-top right) in particular displays very good pedestrian accessibility despite its high altitude. This is however a very densely populated and well serviced area.      Figure 1. Topography of Coimbra (left) and effort-based walking accessibility map (right). The geographical dispersion of the opportunities throughout the city also contributes to the good performance of the indicator: indeed, while some opportunities require climbing, others require descending. In the end, the index for central locations is not excessively penalized by relief effects. On the other end of the spectrum lie the faraway regions of the outskirts. These have worse indexes, but this is essentially related to lack of close opportunities rather than relief effects.   The relief effect is however not negligible: it is present as a background value throughout the study area and becomes more explicit for some higher locations within the central area. For instance, the University campus ‘Polo I’ zone (center of map, near the river) exhibits slightly lower accessibility, owing to being on the top of a hill. The same happens in a few other central locations, which would show better indexes if their altitude were lower. 3. CONCLUSIONS AND FUTURE WORK The methodology proposed here shows that for the hilly city of Coimbra, Portugal, centrality, more than relief, is the chief factor determining a location’s pedestrian Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J.  6  accessibility. This methodology, based on classic definitions of accessibility as disutility and using on human effort (as measured by muscular energy spent to walk the streets network) as impedance, is general and can be applied to any city. Since human effort rises considerably with slope, it especially adequate to hilly cities.   For hilly cities, effort/energy-based pedestrian accessibility maps are, in principle, more accurate than maps based purely on distance. Therefore, these maps should be preferred by municipal authorities when planning for changes to public transportation routes. For the case of Coimbra, busses from the outskirts into the (high accessibility) riverside downtown are frequent, but this is not the case for the Olivais area, whose high pedestrian accessibility indexes indicate it should perhaps be better serviced. Such maps also indicate the best zones to improve sidewalks and crossings, thus providing people with adequate infrastructure for exerting their choice for the pedestrian mode, which is key to foster that choice.  As future work, it would be interesting to apply the methodology to other hilly cities and compare altitude charts with the resulting pedestrian accessibility map, so as to check to what extent the conclusion that centrality dominates over relief effects holds. Another possible line of research would be to set all slopes to zero, recalculate the pedestrian accessibility index and create a ‘flat vs real’ differential map. This map would identify the geographic locations i for which relief is more relevant. The impedance function can also be refined by including sidewalk availability and pavement condition, both of which can influence effort. The effort/energy-based approach also allows for construction of other types of pedestrian accessibility indexes, such as e.g. number of opportunities within standard walking distances (say 600 m), converted into energy equivalent. Finally, since long trips can induce tiredness, to validate the accuracy of the hypothesis that human effort is cumulative, real experiments can be carried out, that involve volunteer pedestrians carrying out a smartphone and a wearable health device to log energy expenditure. (Doing this for short trips would only reproduce the results of [7].) ACKNOWLEDGEMENTS This work was partially supported by the Portuguese Foundation for Science and Technology under grant PEst-OE/EEI/UI308/2014. REFERENCES [1] J. Woodcock, D. Banister, P. Edwards, A.M. Prentice and I. Roberts, “Energy and transport”, Lancet Vol. 370, No. 9592, pp. 1078-1088, (2007). DOI: 10.1016/S0140-6736(07)61254-9 [2] P. Morais and A.S. Camanho, “Evaluation of performance of European cities with the aim to promote quality of life improvements”, Omega Vol. 39, No. 4, pp. 398-409, (2011). DOI: 10.1016/j.omega.2010.09.003 [3] H. Millward, J. Spinney and D. Scott, “Active-transport walking behavior: Sousa, N., Moreira, F.A. and Coutinho-Rodrigues, J.  7  destinations, durations, distances”, J. Transp. Geogr. Vol. 28, pp. 101-110, (2013). DOI: 10.1016/j.jtrangeo.2012.11.012 [4] P.N. Seneviratne, “Acceptable Walking Distances in Central Areas”, J. Transp. Eng. Vol. 111, No. 4, pp. 365-376, (1985). DOI: 10.1061/(ASCE)0733-947X(1985)111:4(365) [5] T.M. Rahul and A. Verma. “A study of acceptable trip distances using walking and cycling in Bangalore”, J. Transp. Geogr. Vol. 38, pp. 106-113, (2014). DOI: 10.1016/j.jtrangeo.2014.05.011 [6] K.T. Geurs and J. Ritsema van Eck, Accessibility measures: review and Applications, Rijksinstituut voor Volksgezondheid en Milieu (National Institute of Public Health and Environment), RIVM report 408505 006, (2001). Weblink: https://rivm.openrepository.com/rivm/bitstream/10029/9487/1/408505006.pdf [7] A.E. Minetti, C. Moia, G.S. Roi, D. Susta and G. 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An energy-based pedestrian accessibility indicator

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